The spiralling cost of car insurance premiums could be curbed if the government clamped down on whiplash claims and insurers were banned from selling on customer information, according to MPs.

In a report, the transport select committee warned that soaring premiums are "primarily the result of market dysfunction and, in particular, the escalation of uncontested claims for whiplash injury".

According to the Association of British Insurers, whiplash claims are now costing insurers and customers more than £2bn a year. This adds an extra £90 to the average motor insurance premium.

Over the last three years, says the ABI, the number of people claiming whiplash has jumped by 32% to 570,000 a year, but the number of accidents reported (less than 210,000) has fallen by 16%.

The transport committee called for the government to raise the threshold for the payment of any compensation in whiplash cases. "If the number of such claims does not fall significantly, the government should bring forward primary legislation to require objective evidence – both of a whiplash injury and of it having a significant effect on the claimant's life – before compensation is paid," said Louise Ellman, the committee's chair.

"The insurance industry must abandon sharp practices that push up premiums, such as passing drivers' personal data to other parties or taking secretive referral fees from solicitors, garages and car hire firms," she added.

The ABI welcomed the report, but said it did not go far enough. Nick Starling, the ABI's director of general insurance, said: "It is absolutely critical that Britain's whiplash epidemic is tackled once and for all, and the select committee's acknowledgment that the bar to receiving compensation for whiplash is too low is a step in the right direction."

However, he added: "Referral fees should be banned altogether and not made more transparent – and that ban should apply to all organisations receiving them, not just insurers. Banning referral fees and, crucially, reducing legal costs will improve the situation for customers.

The Legal Aid, Sentencing and Punishment of Offenders Bill currently going through parliament contains a proposed ban on lawyers and solicitors receiving referral fees, but in road accidents customer details are also routinely sold by insurers, garages, car hire firms and even the police to claims management companies and personal injury lawyers. In June, the former justice secretary, Jack Straw, described this practice as a "dirty secret" and a "racket". The ABI has long lobbied ministers to ban referral fees across the board. The Office of Fair Trading announced last month it would look into the issue as part of a market study.

However, John Spencer, director of Spencers Solicitors, who has been campaigning for reform to the personal injury system, said: "Although whiplash claims are notoriously difficult to accurately diagnose, the suggestion by insurers that there is no objectivity in assessment for the injury is wholly flawed... Insurers often make offers without requiring any medical evidence. Their hope is that they can 'buy off' a claim before the injured person seeks independent legal advice and is properly represented.

"While they clearly do not intend to increase claim numbers, it is in large part an unintended consequence of their own actions."

• This article was amended on 15 February 2012. The original said that lawyers and solicitors have been banned from receiving referral fees in the recent Legal Aid, Sentencing and Punishment of Offenders Bill currently going through parliament. This has been clarified. In addition, insurers have been added to the list of those who routinely sell road accident customer details to claims management companies and personal injury lawyers.